Abstract
Let q be a cube-free positive integer and χ(modq) be a non-principal Dirichlet character. Our main result is a Burgess-type estimate for σ n∈A χ(n), where A ⊂[1,q] is the union of s disjoint intervals I 1, ⋯,I s. We obtain a nontrivial estimate for the character sum over A whenever |A|s -1/2 >q 1/4+ε and each interval Ij (1≤j≤s) has length |I j |>q ε for any ε>0. This follows from an improvement of a mean value Burgess-type estimate studied by Heath-Brown [Number Theory and Related Fields, Springer Proc. Math. Statist. 43, New York (2013), 199-213].
Original language | English |
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Pages (from-to) | 3017-3026 |
Number of pages | 10 |
Journal | Forum Mathematicum |
Volume | 27 |
Issue number | 5 |
DOIs | |
State | Published - Sep 1 2015 |
Bibliographical note
Publisher Copyright:© 2015 by De Gruyter.
Keywords
- Character sum
- harmonic analysis
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics